Net Lagrangian-Based Singularity

 When a given arbitrary Noether-Based mass-bearing cohesive set of discrete energy quanta, is to undergo a net Lagrangian-Based Chern-Simons singularity, to where it is here to be exhibiting an alteration in more derivatives of motion, than the number of spatial dimensions that it is here to be traveling through, then, such an inferred "team" of mass-bearing energy, is here to have a relatively high likely-hood, at the moment at which such a said mass-bearing set of energy, is to be passing through the general locus of such a stated singularity, to be working to bear a spur in the gauge-metric-related motion, of its directly corresponding i*PI(del) Action. TO BE CONTINUED WITH THE SUSPENSE LATER! SINCERELY, SAM ROACH.

Hermitian Expansion From Origin -- Slater-Related Escalation

 If an eigenstate that is to be moving away from its origin, is to work to bear a hermitian expansion in two spatial dimensions, over a given arbitrary discrete duration of time, -- then, the tangential flow of the motion of such a said departing eigenstate, will consequently often tend to work to bear an asymptotic Slater-related escalation. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH. (1989).

Influence Of Dimensional Compactification Upon The Formation Of Chern-Simons Invariants

Let us initially consider a given arbitrary perturbative tense of an orbifold eigenset, that is here to be going through two different successive stages of motion -- over the course of two correlative respective succeeding relatively brief time periods. During the first of these said stages, the superstrings of discrete energy permittivity that work to comprise the said tense of an orbifold eigenset -- are to bear a correlative arbitrarily considered number of spatial dimensions.  After this just mentioned first stage of motion, in which such a tense of an orbifold eigenset is here to be in the process of being transferred along a Lagrangian-based path in time and space, -- the inferred eigenset of such a respective case, is then to bear a similar tense of motion as before -- except that such a cohesive set of superstrings, are then to spontaneously alter into a tense of ensuing to work to bear a lower number of spatial dimensions in time and space.  This means that the respective correlative orbifold eigenset of this particular case scenario, is here to have just been spontaneously spatially compactified into then having a smaller tense of dimensionality.  So; if basically all of the other pertinent factors of such a spatially translated cohesive set of discrete energy quanta, are to remain the same -- except for that alteration or perturbation as to here working to involve a decreased number of spatial dimensions of which such an inferred orbifold eigenset is thence to have, -- then, this will consequently tend to work to allow for the condition of a lowered scalar amplitude in that rate, by which the perturbation of those correlative Chern-Simons Invariants, that are here to be directly associated with the activity of such a said orbifold eigenset, are thence to be formed. I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.

Decompactification Versus Compactification

What I term of as being decompactification, is the inverse of the process of what is known of as being compactification.  So; when a phenomenology is to be of a similar but different nature, yet, to where, it is to alter into having either Less spatial dimensions and/or involving Less correlative directorals, this is the general process of a dimensional/directoral-related Compactification; yet, when a phenomenology is to be of a similar but different nature, yet, to where, it is to alter into having either More spatial dimensions and/or More correlative directorals, this is what I term of as being the general process of a dimensional/directoral-related Decompactification. Sam Roach.

Interesting Stuff As To Grobner Bases

Let's consider what is meant to be determined as a Grobner Basis:

Let's say that one is to have a point particle.  It is theoretically to be of zero spatial dimensions.  Consequently; its surrounding spatial dimensionality, is theoretically here to be "infinite" in its number of spatial dimensions.  Next; one may take certain basic differential geometrical-related mathematical stipulations, about the dimensional relationships of certain spaces, that are here to be related to both the existence and the motion of such a theoretical point particle, both as to what may potentially be an element of what, what may be in union to what, what may intersect what, etc., -- based upon the basic mathematical operations of addition, division, multiplication, and subtraction.  Consequently; one may then work to determine an eigenbasis, that is here to work upon a given arbitrary space, in a Laplacian-related manner -- that is here to work to involve a stipulation, that involves the relationship of one point particle To a stipulation that involves the relationship of another point particle, -- to where the relationship that is here to work to involve the two inferred point particles, is then to be of either a Real Riemann Gaussian-related association, or of a Li-based Gaussian-related association.  Such a general tense of an eigenbasis, may then be utilized, to work to determine as to what actual point-like spaces are more likely to be relatively adjacent to other actual point-like spaces, -- given how such point-like spaces are here to be acting, over time. Such a general tense of an eigenbasis, may be thought of as a Grobner Basis.  Sincerely, Samuel David Roach.

Dimension Of Superstring And Wobble

The greater that the number of spatial dimensions is to be, of any one given arbitrary superstring of discrete energy permittivity -- as when taken over the course of any one given arbitrary respective iteration of BRST, -- the more of a relative scalar amplitude that such a said superstring of discrete energy permittivity will consequently tend to wobble by, when this is here to be considered over the course of a covariant iteration of group-related instanton. To Be Continued! Samuel David Roach.

Part Of What May Happen To Work To Cause Tachyonic Motion

When a superstring of discrete energy permittivity is to be both vibrating anharmonically in an odd number of spatial dimensions in the relative forward-holomorphic direction, at the duration that is right before instanton, and if, as well, the here mentioned superstring of discrete energy permittivity is to be vibrating harmonically in an odd number of spatial dimensions in the relative reverse-holomorphic direction, during the ensuing proximal local Regge Action, then, such a so-mentioned superstring of discrete energy permittivity, will then ensue to become of a tachyonic manner.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

A Little About Partially Complex Manifolds

Let us now consider two different orbifold eigenets -- that work to bear some spatial dimensions in common, yet to where these are to as well to bear some spatial dimensions that are not in common as well.  Let us next say, that these two different said orbifold eigensets, are to bear a certain Gaussian relationship -- when this is taken among those spatial dimensions that these work here to bear such a so-eluded-to Yukawa relationship, that brings these into an extent of being in common with one another.  Yet, let us as well say, that those spatial dimensions that these do not have in common, are here to not be of a Real Reimmanian nature to one another -- to where these two so-eluded-to sets of coherent spaces are not to be fully of a Gaussian-related nature to one another.  This would then work to mean, -- that some of the attributes of one of the so-eluded-to manifolds of coherent spaces, are of a Real-based Gaussian nature to the other so-eluded-to manifold of coherent spaces, while some of the respective attributes of one of the so-eluded-to manifolds of coherent spaces are not of a Real-based Gaussian nature to the other so-eluded-to manifold of coherent spaces.  One may then say, that the two different said manifolds of coherent spaces, -- that are here to act as two different orbifold eigensets -- may be described of as being partially complex manifolds, the one to the other.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Complex Manifolds -- What These Are

One given arbitrary Ward-Cauchy-related manifold is purely a complex phenomenology, when in relation to another given arbitrary Ward-Cauchy-related manifold --- when the two different respective manifolds, do not work to share any of the same spatial dimensions as each other.  Yet, -- one given arbitrary Ward-Cauchy-related manifold is at least partially a complex phenomenology, when in relation to another given arbitrary Ward-Cauchy-related manifold -- when the two different respective manifolds, do not work to share exactly the same spatial dimensions as each other, -- even though such manifolds may, in this second mentioned correlative case scenario, share at least some of the same spatial dimensions as each other.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Some Stuff As To Dimensional Contraction And Orbifold Eigensets

When one superstring of discrete energy permittivity that is of one given arbitrary orbifold eigenset, is to either comapctify or to decompactify by a specific number of spatial dimensions, at a specific instance of time -- then all of the superstrings of discrete energy permittivity, that work to comprise the said orbifold eigenset, will then tend to respectively compactly/decompactify by that same said specific number of spatial dimensions, at that said specific instance of time.  Therefore, if one specific superstring of discrete energy permittivity, that is of one given arbitrary orbifold eigenset, at right before an iteration of BRST, is to vibrate annharmonically by a specific number of spatial dimensions, in a holomorphic manner, at that so-eluded-to proscribed iteration of gauge-metric -- then all of the superstrings of discrete energy permittivity that work to comprise the said orbifold eigenset, will then tend to vibrate annharmonically by that same specific number of spatial dimensions, in a holomorphic manner, at that so-eluded-to proscribed iteration of gauge-metric.  Furthermore -- if one specific superstring of discrete energy permittivity that is of one given arbitrary orbifold eigenset, during the Regge Action, is to vibrate annharmonically in a specific number of spatial dimensions, in an antiholomorphic manner, at that so-eluded-to proscribed iteration of gauge-metric -- then all of the superstrings of discrete energy permittivity, that work to comprise the said orbifold eigenset, will then tend to vibrate annharmonically by that same specific number of spatial dimensions, in an antiholomorphic manner, at that so-eluded-to proscribed iteration of gauge-metric.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Beti Action and Annharmonic Vibration Of Superstrings

If a superstring of discrete energy permittivity is to be vibrating annharmonically in a holomorphic manner, in an odd number of spatial dimensions right before BRST, -- then it will tend to not work to bear a homeomorphic field between itself and its counter-string, during the immediately ensuing correlative Beti Action eigenstate.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Annharmonic Vibration And Tachyonic Flow

So -- if one given arbitrary superstring of discrete energy permittivity, is to both vibrate annharmonically in an odd number of spatial dimensions in a holomorphic manner right before an iteration of BRST, --  as well as vibrating annharmonically in an odd number of spatial dimensions in an antiholomorphic manner during the immediately ensuing iteration of the directly corresponding Regge Action eigenstate, -- then, that respective given arbitrary superstring will then tend to become tachyonic.  When one or more superstrings are to become tachyonic -- then, these will undergo at least a moment of tachyonic flow.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Special Derivation

I derived the value "3.026*10^(-32)Kilograms" at the beginning part of my earlier formula, from the condition -- that the mass of a neutrino-based orbifold eigenset is of the value of 17,000 electron volt's eqivalent worth of mass.  An electron volt's equivalent worth of mass is 1.78*10^(-36) Kilograms.  17,000*1.78*10^(-36) Kilograms is 3.026*10^(-32) Kilograms.
Force is proverbially mass times acceleration.  If one were to take the mass of a typical neutrino-based orbifold eigenset, -- and if one were to make this to travel with a tense of a "pulse" of 1 meters cubed per second squared, (like a force, yet in terms of "meters cubed" per second squared instead of in terms of "meters" per second squared, since the macroscopic world is to bear the perverbial three spatial dimensions plus time) -- and if one were to then to multiply the latter by the said mass of a typical neutrino-based orbifold eigenset, -- then, one would then bear to have a value of "3.026*10^(-32)Kilograms*Meters Cubed/Seconds Squared.
The maximum mass of an individually taken neutrino-based superstring is, though, only a fraction of an electron volt's equivalent worth of mass.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Knotting And Instanton

If the absolute value of the respective Betti number, that is here to be displayed right before any one given arbitrary iteration of instanton -- as this may here be applicable to any one respective given arbitrary superstring of discrete energy permittivity -- is to here to not be equal to the correlative absolute value of the respective Betti number, that is here to be displayed during the directly corresponding duration of the Regge Action that is here to happen just after BRST (just after a vast majority of the duration of the so-eluded-to iteration of instanton), then, the said superstring of discrete energy permittivity will here work to bear indices of cohomology that are here to bear a higher scalar amplitude of knotting -- during the said directly corresponding duration of the Regge Action, --  than the amount of a scalar amplitude of knotting that such a said index-related tense of cohomology that is produced by a superstring of discrete energy permittivity, had then to have displayed from the cohomology that it had produced from right before the said directly correlative iteration of BRST.  This is directly associated with the condition, if this is here to be a case of a superstring that is directly in the process of Noether Flow -- that a superstring of discrete energy permittivity, that is to be in the process of working to alter in the scalar magnitude of the number of spatial dimensions that it is here to display, will compactify in dimensionality right before instanton, -- while such a said superstring will decompactify in dimensnionality during the directly corresponding duration of the Regge Action. (This is in consideration of the Ward-Cauchy-related condition, that the Regge Action happens right at the end of any one respective given arbitrary iteration of instanton).
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Net Exchange Of Partition-Related Discrepancies

If the Lorentz-Four-Contraction of a phenomenology of mass-bearing superstrings is to be maintained over time -- to where the correlative Polyakov Action eigenstate, that is of the self-same phenomenology of mass-bearing superstrings, is here as well to be maintained over that same period of time, -- the number of partition-related discrepancies that the said phenomenology of mass-bearing superstrings is to gain per each individually taken instanton, will tend to equal the number of partition-related discrepancies that the so-stated phenomenology of mass-bearing superstrings will lose per each individually taken instanton -- over the said duration of time.  This will then mean, that the directly corresponding absolute value of the Beti number per instanton -- that is here to be correlative to the directly corresponding scalar amplitude of spatial dimensional compactification, will here tend to be equal to that directly corresponding absolute value of the Beti number per instanton -- that is here to be correlative to the directly corresponding scalar amplitude of spatial dimensional decompactification, -- over the so-eluded-to evenly-gauged Hamiltonian eigenmetric, that is here to correspond to the said time period of such a said case.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

More About Discrete Residual Energy Released As Photon

As I have mentioned before, and as it is quite already known in physics -- when electromagnetic energy is to strike an electron, the said electron is here to have a tendency of jumping back-and-forth energy levels, in so as to release its residual kinetic energy in the form of a photon.  As the just mentioned photon is in the process of being formed by the so-stated released residual kinetic energy of an electron, -- the directly corresponding electron that is here to be moving back-and-forth an energy level, in the process of indirectly working to form a discrete increment of light, that is in the form of an impending photon -- (the said electron) will here to tend to be re-bounding via the motion of a Ward-Supplemental-related manner, in the process of going from a condition of moving inward an energy level, into then going into a condition of moving outward an energy level.  Such a re-bounding Fourier-related activity, that is here to work to involve a Ward-Supplemental process, is here to then involve a set of  antiholomorphic Kahler conditions -- which, to an extent, is dependent upon the number of superstrings that work to comprise the overall electron, that is here to act as one respective overall orbifold eigenset, that is present at that given arbitrary electron's energy level and so forth, from within the given arbitrary atom of the said respective case.  Such a set of antiholomorphic Kahler conditions, is to then to rise in so as to form a set of Lagrangian-based Chern-Simons singularities, -- of which will then bear a set of complex roots, depending upon the number of spatial dimensions that the said electron is to be going through, as it is here to be traveling in a back-and-forth manner over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

More As To The Nature Of Fadeev-Popov-Trace Eigenstate Composition

The relative tense of the non-Lorentz-related compactification of mini-stringular segmentation, that is of any given arbitrary Fadeev-Popov-Trace eigenstate, is to bear a scalar amplitude of being of a factor of five away from being fully compactified at the beginning of BRST.  Such a lack of compactification, works to allow for the feeding-in of mini-stringular segmentation -- as is it is to ever be necessary.  Such an eigenstate of this general  genus of trace, is to be virtually closed at each endpoint.  The correlative Fadeev-Popov-Trace eigenstate, that is correlative to a one-dimensional superstring of discrete energy permittivity, is to bear five second-order light-cone-gauge eigenstates, that are here to be inter-woven with the correlative superstring, whereas, the correlative Fadeev-Popov-Trace eigenstate that is correlative to a two-dimensional superstring of discrete energy permittivity, is to bear ten second-order light-cone-gauge eigenstates, -- that are inter-woven with the correlative superstring.  This is not to be confused with the Ward-Cauchy-based condition, that any Calabi-Yau state will tend to move through between four and 32 spatial dimensions plus time -- per each ensuing successive series of group-related instanton.  A typical  superstring of discrete energy permittivity that is not of a hook-like string, will tend to iterate at BRST, -- in a tense of what is to act as being of either one or two spatial dimensions plus time.  Yet, over the course of both the ending portion of instanton, as well as during the generally unnoticed duration of Ultimon Flow, -- any respective superstring will be moving through a Hamiltonian operand, that will here work to include multiple ulterior spatial dimensions besides the generally related ones that I have just eluded to.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part Three of the Last Test Questions for Course 17 -- the Ricci Scalar

10)  Light has three Real Reimmanian-based spatial dimensions.  This is due to the Ward-Caucy conditions that exist above the atomic level -- these of which utilize only three spatial dimensions plus time.   (Yet, since the nucleus of an atom has an f-field (4 spatial dimensions plus time), in a way, photons exist in four Real Reimmanian spatial dimensions plus time.)

11)  Light works to bear a minimum of ten spatial dimensions plus time.  This so-eluded-to spatial dimensionality bears four stretched-out spatial dimensions plus six curled-up spatial dimensions.  So, at the sub-atomic level, light bears four Real spatial dimensions Plus six Njenhuis curled-up spatial dimensions plus time.  This is equivalent to the summation of the number of spatial dimensions of an f-field plus the number of spatial dimensions of a d-field.

A Little As To World-Tubes

The following knowledge is on the nature of superstrings.:  One main world-tube is near another main world-tube.  Each of the prior mentioned world-tubes is conprised in part by one and two-dimensional superstrings.  Each one-dimensional superstring that I just mentioned bears a two-dimensional field.  Each two-dimensional superstring that I recently mentioned bears a three-dimensional field.  So, two-dimensional superstrings form world-sheets that bear a minimum of three spatial dimensions, while one-dimensional superstrings form world-sheets that bear a minimum of two spatial dimensions.  Both one and two-dimensional superstrings work to form world-sheets via the physical  mapping as to where these said strings were at -- in terms of what had happened in the substringular in the relatively transient past, relative to where the said superstrings are at in terms of their simultaneaous position aver a set conimetric.  The just mentioned world-sheets are differentially associated to each other as a function of their degree of covariant kinematic codifferentiation.  The positive-ground-states that here exist in the form of partitions are arranged at the center-state of the linkages that are binding, via the toroidal-like nature of the related world-sheets that are formed by the mapping of the trajectory of the said related superstrings over a sequential series of instantons.  The kinematic re-delineation of superstrings works to form the locus of their inter-relative covariant codifferentiation over time.  This post works to show -- to a mild extent -- the inter-relationship type of basis of every superstring, in some form or another, toward all of the other stings over time, and, time is the interaction of phenomena over a sequential series of instantons.